Answer: they sold 3000 adult tickets and 1200 children tickets.
Explanation:
Let x represent the number of adult tickets that they sold.
Let y represent the number of children tickets that they sold.
The theatre sold a total of 4200 tickets. This means that
x + y = 4200
An adults ticket costs 10 dollars and a child's ticket costs 5.5 dollars. The
theater had a revenue of 36,600. This means that
10x + 5.5y = 36600- - - - - - - - -- -1
Substituting x = 4200 - y into equation 1, it becomes
10(4200 - y) + 5.5y = 36600
42000 - 10y + 5.5y = 36600
- 10x + 5.5y = 36600 - 42000
- 4.5y = - 5400
y = - 5400/ - 4.5
y = 1200
x = 4200 - y = 4200- 1200
x = 3000